[susan53]

There are two different meanings here.

1) To be/get on top of something usually means to have it under control. Eg : When I got back from my holidays I had 300 hundred e-mails waiting for me. It took me three days to get on top of them. - ie to deal with them all, or to reduce them to a manageable number. So, if someone "on top of" their game, it means that they have the situation under control. You often find it used where someone has previously had problems but has now resolved them. When I googled "on top of his game", I found eg an example of a football coach who'd had a stroke and lost the ability to speak, but had recovered and made a comeback; another about a cricketer who was plagued by injury for years, but again made a comeback; and a third about a farmer who, despite innumerable problems in the market and in his own life, has made a successful career as a wool producer. So notice that "game" isn't always used literally - ie referring to a sport. It can sometimes also be used idiomatically to mean your profession or whatever it is that you do.
Slightly differently, there is also the idiom to be/feel on top of the world, meaning to be/feel very happy : When I found out I'd passed the exam I was on top of the world!

2) To be at /get to/work your way to (etc) the top of a profession, on the other hand, means to be one of the best : He's only a junior manager at the moment, but he's determined to get to the top / Federer was at the top for a long time, but now Nadal has taken over.
Top can also be used as an adjective in this way : He's one of the top doctors for his speciality.

Hope that helps.